The Malthusian growth model - GitHub Pages

The Malthusian growth model

Paulo Brito pbrito@iseg.ulisboa.pt

3.3.2021

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Malthusian theory

Popular definition of "Malthusian economics" : population growth exponentially and food grows linearly

This would lead either to catastrophe or to the existence of natural (not nice) stabilization mechanisms, in the absence of "moral restraint"

The idea there is an endogenous mechanism relating population and wages is consistent with events in pre-industrial W. Europe

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Wages and population in historical data

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Malthusian theory

We will see that the existence of marginal decreasing returns to labor is a necessary (although not sufficient) condition.

The idea that the existence of a fixed resources and decreasing returns to production implies that growth processes eventually stop is present in most Classical economists (Quesnay, Smith, Ricardo, Marx) and, possibly, in modern ecologists.

But it was Thomas Malthus who stated it more clearly in An Essay on the Principle of Population (1798) and systematically gathered data to sustain it.

We next provide a modern view of the theory

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Malthusian model

The general idea: It presents the joint dynamics of production and population growth In pre-industrial societies: there are two main factors of production labor and land Labor is the reproducible factor of production (no capital accumulation, no R&D) The basic dynamic mechanism is: increase in income leads to increase in population and in labor supply; this increases aggregate income, but income per capita does not increase at the same pace, leading eventually to a steady state (positive extensive effect but negative intensive effect). Decreasing marginal returns for the reproducible factor is the main driving force behind the non-existence of growth in the long run. The conditions for the existence of long run growth are very specific (learning-by-doing)

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Assumptions

Production:

production uses two factors: labor and land the production function has constant returns to scale the only reproducible factor is labor, and it faces decreasing

marginal returns

Population:

fertility is endogenous and mortality is exogenous

Farmers:

households are land-owners they choose among consumption and child-rearing there are no savings

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X (land)

F(L(t), X)

Y(t)

L(t) (labor)

v(y(t))

c(t)

L (b(t), m(t))

b(t) (fertility)

m (mortality)

v(y)

=

max{u(c, b)

:

c+

pb

y}

and

y

=

Y L

where

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The model

Production

Production function Y(t) = (AX)L(t)1-, 0 < < 1

where: A productivity, X stock of land, L labor input displays constant returns to scale

(AX)(L)1- = Y

implication: the Euler theorem holds Y = YL + YX L X

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